Collective bending motion of a two-dimensionally correlated bowl-stacked columnar liquid crystalline assembly under a shear force

Stacked teacups inspired the idea that columnar assemblies of stacked bowl-shaped molecules may exhibit a unique dynamic behavior, unlike usual assemblies of planar disc– and rod-shaped molecules. On the basis of the molecular design concept for creating higher-order discotic liquid crystals, found in our group, we synthesized a sumanene derivative with octyloxycarbonyl side chains. This molecule forms an ordered hexagonal columnar mesophase, but unexpectedly, the columnar assembly is very soft, similar to sugar syrup. It displays, upon application of a shear force on solid substrates, a flexible bending motion with continuous angle variations of bowl-stacked columns while preserving the two-dimensional hexagonal order. In general, alignment control of higher-order liquid crystals is difficult to achieve due to their high viscosity. The present system that brings together higher structural order and mechanical softness will spark interest in bowl-shaped molecules as a component for developing higher-order liquid crystals with unique mechanical and stimuli-responsive properties.


INTRODUCTION
Since efficient synthetic methods for buckybowl molecules (i.e., subunits of C 60 ) such as sumanene (1)(2)(3)(4)(5)(6) and corannulene (7)(8)(9)(10)(11) have been established, bowl-shaped and curved π-conjugated molecules have attracted considerable attention (12)(13)(14). The major incentive for the development of nonplanar π-conjugated molecules lies in the exploration of unique properties different from those expected for planar systems. For example, bowl-shaped molecules have a dipole moment in the out-of-plane direction arising from the difference in electrostatic potentials between their concave and convex faces (12). They can also undergo bowl-to-bowl inversion accompanied by dipole inversion (12). In addition to the single-molecular properties, sumanene derivatives, in particular, are reported to form ordered one-dimensional (1D) columnar structures, similar to planar π-conjugated molecules, with convex-concave bowl stacking, providing an efficient charge-transport pathway (15,16). When bowl-to-bowl inversion is allowed in such bowl-stacked columns, a ferroelectric response could be achieved, as recently demonstrated for a columnar liquid-crystalline assembly of heterasumanene (17), where the dipole aligns with the bowl inversion in the direction of the applied electric field. Besides the dynamic properties arising from bowl-to-bowl inversion, it is expected that there are still uncovered behaviors, which could be derived from the characteristic shape of a bowl.
Inspired by stacked teacups in the university cafeteria, we wondered whether another mode of motion characteristic of bowlstacked columnar assemblies, namely, bending motion, might be present. Figure 1 (A and B) shows a simple geometrical consideration of the behaviors of columnar assemblies associated with possible movements of discotic and bowl-shaped molecules. In both cases, in-plane rotation would be allowed. When considering translational displacement and angular variation, these motions should cause the disruption of columnar assemblies composed of discotic molecules (Fig. 1A). However, in the case of a bowl-stacked column (Fig. 1B), the translational displacement of the constituent molecules would be more constrained than in the discotic case, while angular variation in which the column does not collapse but bends to accommodate the molecular movement can easily occur. Accordingly, a bowl-stacked column is expected to show a flexible bending motion, which would not occur in similar columns composed of planar discotic molecules.
To test the above idea, it is reasonable to use a liquid-crystalline material that allows examination of the orientation and motion of the columns macroscopically. Such a bowl-stacked columnar LC must also uniformly align on a solid substrate over a large area, rather than one containing randomly oriented microdomains. However, hitherto known bowl-stacked columnar LCs do not show spontaneous and uniform alignment on a solid substrate (18,19). For constructing an ideal system, we took a design clue from triphenylene hexacarboxylic ester (TE)-based columnar LCs, which exhibit spontaneous and uniform homeotropic alignment on various solid substrates (20). A TE derivative with chiral side chains was found to form a macroscopic fluid droplet with single crystal-like structural order (21). Very recently, we demonstrated that a TE derivative (TE f , Fig. 1C) with semifluoroalkylated side chains not only spontaneously aligns homeotropically on solid substrates in its Col h mesophase but also undergoes homeotropicto-homogeneous alignment switching upon application of a shear force (22). The above mesophase behaviors have not yet been reported for extensively studied columnar LCs, e.g., those derived from hexaalkoxytriphenylenes.
In the present study, we synthesized sumanene hexacarboxylic esters SE n (n = 1, 8, and 10; Fig. 1D) with long alkyl side chains. Depending on the length of the side chain, SE n were obtained as crystalline (n = 1), viscose fluid-like (n = 8), and again crystalline (n = 10) materials at room temperature, and only SE 8 exhibited a liquid-crystalline mesophase characterized by an ordered hexagonal columnar (Col ho ) phase. Notably, in sharp contrast to usual discotic Col ho LCs, SE 8 at the mesophase temperature is very soft, like sugar syrup. Furthermore, in an LC film sample prepared on a solid substrate, the bowl-stacked columns of SE 8 not only align homeotropically over the entire film but also undergo continuous homeotropicto-(quasi)homogeneous alignment changes upon mechanical shearing. Encouraged by these unique properties of SE 8 , we conducted detailed experimental investigations using polarized optical microscopy (POM) and in situ x-ray diffraction (XRD) to clarify how the LC with the bowl-shaped mesogen behaves under application of a mechanical force. Through this paper, we show that bowl-shaped molecules have great potential for developing higher-order LCs with unprecedented mechanical properties and responsiveness, which are difficult to achieve using conventional rod-shaped and discotic mesogens.

Molecular dynamics calculations
To gain intuitive understanding about the difference between columnar assembles of bowl-shaped and planar disc-shaped molecules (Fig. 1, A and B), we performed molecular dynamics (MD) calculations for bowl-stacked and π-stacked dimer models of SE 1 (Fig. 1D) and TE 1 (20) (Fig. 1C), respectively. We used the initial geometries taken from the crystal structures of SE 1 (vide infra) and TE 1 (Fig. 2A). As a measure of deformation of the dimers, we defined the angle (θ) between the two normal vectors u 1 and u 2 relative to the central six-membered rings of the upper and lower molecules, respectively ( Fig. 2A). Deformability of the dimers can be evaluated using a potential of mean force (PMF). We define the probability distribution function [P(θ)] of finding a dimer with respect to θ, and PMF is expressed as F(θ) = -k B TlogP(θ), where k B and T are the Boltzmann constant and temperature, respectively. By means of ab initio MD (AI-MD) calculations, P(θ) values were calculated by sampling the atomic configurations of SE 1 and TE 1 . Figure 2B shows plots of PMF for SE 1 (orange) and TE 1 (blue) with a temperature set to 400 K. For both SE 1 and TE 1 , the most stable arrangement was found at θ~0°, which corresponds to linearly stacked 1D columns. While F(θ) for both SE 1 and TE 1 can be described as a monotonically increasing function, the slope of the plots for SE 1 is much smaller than that of TE 1 . For example, the energy value required to reach θ = 5°for SE 1 (0.015 eV) is approximately half of that for TE 1 (0.029 eV). The estimated energy value of thermal fluctuations at 400 K using the calculated model used is 10 −1 eV, for which the θ values for SE 1 and TE 1 are 17°and 9°, respectively (Fig. 2B). Therefore, the bowl-stacked dimer of SE 1 is predicted to have substantially higher deformability in terms of angular variation with respect to the stacking direction compared to the π-stacked dimer of TE 1 . We also plotted PMF with respect to the in-plane relative rotation angle and the centroid-centroid distances between stacked molecules using the same data ( fig. S1). While the former (fig. S1A) is similar for TE 1 and SE 1 , the latter (fig. S1B) shows that the distribution of distances is clearly larger and shifted toward the long-range side for SE 1 compared to TE 1 . The picture obtained from the above simple analysis supports our intuitive prediction that bowl-stacked 1D columns may show a flexible bending motion.

Synthesis and characterization
Methyl ester derivative SE 1 (Fig. 1D) was synthesized by transesterification of 2,3,5,6,8,9-hexakis(phenyloxycarbonyl)sumanene (23) with methanol using Otera's catalyst. Needle-shaped single crystals of SE 1 were grown from a mixture of chloroform and hexane. Single-crystal x-ray analysis revealed that SE 1 forms well-ordered 1D bowl-stacked columns with a staggered geometry through a convex-concave interaction (Fig. 3A, bottom). In all the columns, the convex surfaces of the bowls were aligned in the same direction in a manner similar to unsubstituted sumanene (1). The 1D bowlstacked columns are laterally packed into a quasi-hexagonal structure (Fig. 3A, top).
Using procedures similar to that for SE 1 , SE 10 , and SE 8 (Fig. 1D) were prepared. Differential scanning calorimetry (DSC) and powder XRD analysis showed that the phase diagram of SE 10 involves only crystalline (Cr) and isotropic liquid (Iso) phases ( Fig.  1D and figs. S2B and S3). In contrast, SE 8 exhibited a mesophase between 12°and 47°C upon heating ( Fig. 1D and figs. S2A and S4). The powder XRD pattern of SE 8 at 30°C (Fig. 3B) displayed a strong peak with a d-spacing of 2.00 nm and weak peaks with dspacings of 1.15, 0.75, and 0.66 nm due to diffractions from the (100), (110), (200), and (300) planes, respectively, of a P6mm hexagonal lattice with a lattice parameter (a) of 2.31 nm. A diffraction peak with a d-spacing of 0.42 nm, corresponding to the core-to-core separation between the bowl-stacked sumanene (24), was observed. Thus, the mesophase of SE 8 is assigned to be an ordered hexagonal columnar (Col ho ) phase. Noteworthy is the fact that, despite the formation of a highly ordered structure in the mesophase of SE 8 , the appearance and texture of its bulk sample (Fig. 3C) are very similar to those of sugar syrup (movie S1) and quite different from those of usual discotic columnar LCs. For reference, 2,3,6,7,10,11-hexakis(octyloxycarbonyl)triphenylene (20) (TE 8 , Fig. 1C) is a hard waxy solid in its Col ho mesophase ( Fig. 3D) (movie S2). Figure 4A shows POM images of a film sample of SE 8 (10 μm in thickness) sandwiched between two glass substrates. In the POM under crossed nicols, most of the areas were dark field despite the presence of some slight areas that display birefringence. The OM image showed a dendritic texture, typically observed for homeotropically aligned Col ho LCs ( fig. S5). Thus, SE 8 in its Col ho phase tends to adopt a homeotropic alignment on glass. Nonetheless, as is often observed for liquid-crystalline materials, when the film thickness increases, the alignment behavior deteriorated. For instance, the POM image of a 20-μm-thick film of SE 8 ( fig. S6) indicated the occurrence of randomly oriented multi-domains.

POM measurements
Notably, when a uniaxial shear force was applied to a homeotropically aligned film of SE 8 at 30°C, the POM image of the resultant film became completely dark when the polarizer was arranged parallel or perpendicular to the shear direction (Fig. 4B, θ = 0°or 90°). When the sample stage was rotated by 45°, a bright field appeared ( Fig. 4B, θ = 45°). These observations indicate that the bowl-stacked columns of SE 8 collectively move upon shearing, to change the alignment from homeotropic to homogeneous. In general, Col h LCs with a low 1D-stacking order have low viscosity and can undergo a change in alignment upon application of a shear force, while Col ho LCs feature high viscosity, and it is difficult to change the alignment using external fields. To the best of our knowledge, only two discotic columnar LCs have been reported to show such shear force-induced homeotropic-to-homogeneous alignment switching (22,25), with both examples possessing (semi)fluoroalkyl side chains. Therefore, it is obvious that the mechanical response behavior of SE 8 is not due to an effect of the side chains but originates from the properties of the bowl-shaped mesogen.
For a deeper understanding of the unique behavior of SE 8 , we further investigated the shear-displacement dependence. Figure  5A shows the change in POM images at 30°C for a homeotropically aligned 10-μm-thick film of SE 8 upon continuous shearing at a rate of 1.0 mm s −1 (see also fig. S7 for the experimental setup). When shear displacement (D) was increased (Fig. 5A, shearing process 1), the dark-field regions gradually decreased and bright-field regions appeared. The color tone in the resultant bright-field regions gradually became uniform with a decrease in the number of domain boundaries. Eventually, an almost uniform POM image due to a homogeneous alignment resulted at D = 5 mm. Hence, upon shearing, the direction of the longer axis of bowlstacked columns gradually and continuously changes from perpendicular to parallel with respect to the substrate surface. This behavior is in sharp contrast to that in the Col ho phase of (semi)fluoroalkylated TE derivative (TE f , Fig. 1C) (22), where an alignment change from homeotropic to homogeneous suddenly occurs with a threshold of shear displacement. Moreover, while the resultant homogeneous alignment of TE f can be maintained for a long time as memory, this did not hold true for SE 8 . According to the POM image of a sheared film taken after being allowed to stand for 72 hours at 30°C ( fig. S8), randomly oriented multidomains appear to relieve structural strains caused by the alignment change. We presume that the structural relaxation is likely due to the mechanical flexibility (i.e., large degree of freedom of molecular movement) of SE 8 in the Col ho and a surface anchoring effect that could operate at the material and substrate interface.
When a shear force was applied in the reverse direction to the homogenously aligned film of SE 8 (Fig. 5B, shearing process 2), the overall color of the POM image was changed, with an increase in dark streaks parallel to the shear direction. However, the POM  8 sandwiched between two glass substrates, taken after being heated once to its melting point and then cooled to 30°C (cooling rate, 0.5°C min −1 ). Since the bowl orientation in the Col ho phase cannot be determined, the drawing on the right side is just a schematic, according to the crystal structure of SE 1 , to assist the understanding of readers. (B) POM images at 30°C of a 10-μmthick film of SE 8 after mechanical shearing at 30°C (shear displacement = 10 mm). The small black spots in the right POM image are due to the glass beads (10 μm in diameter) used to adjust the film thickness to be constant. The white arrows represent the transmission axes of the polarizer (P) and analyzer (A). The red arrows and θ indicate the shear direction and angles relative to the transmission axis of the analyzer, respectively. Scale bars, 200 μm. image did not return to the original dark field after the upper glass substrate was returned to the initial position (D = 0 mm, shear process 2). Then, a shear force was applied to the resultant sample in the same direction as shearing process 1 (Fig. 5C, shearing process 3). The change in the POM images during this shearing process is similar to those observed for shearing process 1 (Fig. 5, A and B). Last, a uniform and bright image was generated again at D = 5 mm. These observations indicate that the bowl-stacked columnar assembly of SE 8 can respond flexibly and collectively to the shear force, to allow changes in alignment in the shear direction.

In situ XRD measurements
To investigate the shear-force response of the hexagonal columnar assembly of SE 8 in more detail, we performed in situ transmission (through-view) and reflection XRD measurements while applying a shear force (Fig. 6, A to D, and fig. S9). Figure 6A shows throughview XRD images of a 10-μm-thick film of homeotropically aligned SE 8 sandwiched between a sapphire substrate and a polyimide sheet, measured at 30°C while shearing at a rate of 25 μm s −1 . Consistent with the homeotropic alignment, before shearing (D = 0 mm), diffractions from the (110)  In situ reflection XRD measurements (incident angle of the x-ray beam = 1°; Fig. 6B and fig. S9) provided further insight into how the bowl-stacked columns of SE 8 change the alignment. Before shearing (D = 0 mm), diffraction arcs due to the bowl-stacked sumanene were observed in the out-of-plane direction. Upon shearing, these gradually moved to the in-plane direction (D = 0.5 to 5.0 mm). The shape of the diffraction arcs did not become symmetric even at D = 5.0 mm, with the d values for the diffractions arising from the hexagonal lattice unchanged before and after shearing. Therefore, the bowl-stacked columns of SE 8 are gradually oriented in the direction of shear force without impairing their hexagonal arrangement and eventually converge to a slightly tilted direction relative to the substrate surface. Such a quasi-homogeneous alignment of bowlstacked columns is likely due to a surface anchoring effect, as suggested by the POM observations (Fig. 5).
Then, we applied a shear force to the resultant film at a rate of 25 μm s −1 in the reverse direction to the original. As shown in Fig. 6C, no detectable change was observed for the through-view XRD images at D values ranging from 4.0 to 2.0 mm. On the other hand, in the reflection XRD image (Fig. 6D), the inclination angle of the diffraction arcs in the in-plane direction due to bowl stacking, initially became parallel at D = 3.0 mm but finally inverted at D = 2.0 mm without moving to the out-of-plane direction. Thus, upon application of a shear force in the reverse direction, rather than regenerating a homeotropic alignment, two main homogeneous alignments with an orientation opposite to each other occur. There are two plausible scenarios that can explain the intriguing dynamic behavior of SE 8 in response to shearing; (i) the generation of two bowl-stacked domains with inclination angles opposite to one another (Fig. 6E, i) and (ii) twofold bending of bowl-stacked columns that results in a two-orientation distribution of diffraction arcs in the in-plane direction (Fig. 6E, ii). However, the former scenario is unlikely, given the fact that no feature of domain segregation can be observed in the POM upon application of a shear force in the reverse direction (Fig. 5B). The latter scenario is reasonable when considering that the bowl-stacked column of SE 8 can show a flexible bending motion. Although such bending of a 1D column cannot be expected for usual discotic columnar LCs, it should be possible for a 1D column composed of a bowl-shaped mesogen that has larger degree of freedom in angular variation, as predicted by the MD calculations (Fig. 2). Grazing incidence XRD (GI-XRD) experiments with different angles of the incident x-ray beam provided further information on the structure developed inside the film, supporting scenario (ii) (Fig. 6E, ii). We prepared homeotropically aligned films of SE 8 (10 μm in thickness) sandwiched between a sapphire substrate and a polyimide sheet and sheared at 30°C with displacements of D = 0.0, 0.5, or 3.0 mm. The resultant film was cooled to −80°C, and then the upper polyimide film was peeled off, so that the film surface can be exposed to an incident x-ray beam (Fig. 7, A, D, and G). We confirmed that this cooling process does not affect the columnar alignment inside the film ( fig. S10). As expected, the 2D XRD images of a homeotropically aligned film (D = 0 mm) were identical, regardless of incident angle (Fig. 7, A to C). In contrast, the sheared sample (D = 0.5 mm) showed a clear incident-angle dependence (Fig. 7, D to F). Specifically, as the incident angle of the x-ray beam became shallower from 0.40°to 0.10°, the orientation distribution of diffraction arcs due to bowl stacking, which were tilted to the right, became larger (Fig. 7F). This indicates that the proportion of tilted bowlstacked columns is greater near the surface. For a sheared sample (D = 3.0 mm) in which SE 8 adopts a quasi-homogeneous alignment, the obtained 2D XRD images did not show any incident-angle dependence (Fig. 7, G to I). From these observations, we can conclude that, during the shearing process, the orientation distribution of the bowl-stacked columns continuously changes with respect to the depth from the film surface (Fig. 6E, ii). As already described, the Col ho phase of SE 8 is very soft and even shows a sticky nature (Fig. 3C). Figure 8A shows photographs of a bulk sample of SE 8 on a glass substrate being touched with a glass rod and pulled up (relative heights of the glass rod; h = 0.0 to 3.0 mm). We were curious about how through-view XRD image of the bulk sample changes in the course of the pulling process. At h = 0, diffraction arcs arising from bowl-stacked sumanene were uniformly distributed, meaning that the columnar assembly does not align in any particular direction (Fig. 8B). When the LC sample was pulled up to h = 3.0 mm, the diffraction arcs observed at three different positions became highly oriented along the stretched direction (Fig. 8C). Thus, the bowl-stacked columnar assembly of SE 8 can flexibly change its orientation after an external force is applied. Such orientation flexibility is often observed for lyotropic LCs and polymeric materials but is quite unique for single-component LCs composed of discrete molecules (26).

DISCUSSION
On the basis our previous findings (20)(21)(22), we designed a liquidcrystalline sumanene derivative (SE 8 ) to which alkyl side chains are attached via an ester linkage. We found that SE 8 shows unique softness and remarkable dynamic behavior, which arises from bowlstacking of the sumanene core in its ordered hexagonal columnar (Col ho ) phase. What is particularly interesting is that, following application of a shear force, the 1D bowl-stacked columns of SE 8 undergo a collective deformation while preserving its hexagonal 2D arrangement. In situ POM and XRD observations using specially designed experimental setups allowed us to capture the movements of SE 8 in the Col ho phase.
LCs that have an orientational order of their constituent molecules and alignment-switching ability have attracted much attention in terms of soft matter science and various practical applications (27)(28)(29)(30)(31). However, in LCs, there is an essential trade-off between the dimensionality of structural order and the processability. For instance, nematic LCs with low viscosity and high fluidity can easily be unidirectionally aligned by applying external stimuli including electric fields, magnetic fields, and mechanical shearing (32)(33)(34)(35)(36)(37), whereas the degree of orientation of nematic LCs is generally low (38). In contrast, higher-order LCs such as smectic LCs and discotic hexagonal columnar (Col h ) LCs, in which their constituent molecules assemble with 2D structural correlation, have the advantage of being able to use the intrinsic properties arising from anisotropic molecular alignments (39)(40)(41)(42)(43). However, alignment control and switching are difficult due to their high viscosity, which is close to crystalline in nature (44)(45)(46)(47)(48)(49)(50)(51)(52). This study not only reveals the collective motional behavior of bowl-stacked columns but also demonstrates the utility of bowl-shaped molecules as a mesogen of LCs to achieve both higher structural order and mechanical softness. Considering also recent progress in synthetic technology on curved π-electron systems (12)(13)(14), we believe that the present finding will stimulate the discovery of unexplored mesogens and, in turn, the development of higher-order LCs that exhibit interesting physical and/or stimuli-responsive properties.

Methods
Preparative size exclusion chromatography (SEC) was performed on a Japan Analytical Industry LC-9210NEXT recycling preparative high-performance liquid chromatography system, equipped with JAIGEL-1HH, JAIGEL-2HH, and JAIGEL-2.5H columns and a multiwavelength detector (MD-2010 Plus ) using CHCl 3 as an eluent. Nuclear magnetic resonance (NMR) spectroscopy measurements were carried out on a Bruker AVANCE III HD-500 spectrometer (500 MHz for 1 H and 125 MHz for 13   multiplet (m). Atmospheric pressure chemical ionization-time-offlight (APCI-TOF) mass spectrometry measurements were carried out on a Bruker micrOTOF II mass spectrometer equipped with an APCI probe. Fourier transform infrared (FT-IR) spectra were recorded at 25°C on a JASCO FT/IR-6600 Fourier-transform infrared spectrometer. DSC measurements were carried out on a Mettler-Toledo DSC 1 differential scanning calorimeter, where temperature and enthalpy were calibrated with In (430 K, 3.3 J/mol) and Zn (692.7 K, 12 J/mol) standard samples in sealed Al pans. Cooling and heating profiles were recorded and analyzed using the Mettler-Toledo STAR e software system. POM was performed on a Nikon Eclipse LV100POL optical polarizing microscope, equipped with a Mettler-Toledo HS1 controller attached to a HS82 hot stage. Polarized electronic absorption spectra were recorded on a JASCO V-670 UV/VIS spectrometer equipped with JASCO RSH-744 rotation sample holder and JASCO GPH-506 polarizer.

Through-view XRD measurements for bulk samples
Variable-temperature 1D XRD patterns of bulk samples were measured using the BL44B2 beamline at SPring-8 (Hyogo, Japan) equipped with an imaging-plate area detector (54). The wavelength (λ = 1.08 Å) of the incident x-ray beam was calibrated using cerium oxide (standard reference material 674b). The sample-to-detector distance was 286.5(1) mm. Unless otherwise stated, bulk samples in a glass capillary were measured while spinning at a rate of 100 rpm.

In situ XRD measurements under application of a shear force on a linear motorized stage
In situ XRD experiments on a linear motorized stage (x-stage; XA05A-R101, Kohzu Precision Co.) were conducted using the BL-8A and BL-8B beamlines at Photon Factory (Ibaraki, Japan). A film sample of SE 8 sandwiched between a sapphire substrate and a polyimide sheet was placed on a Instec HTC-402 hot stage, heated once to the melting point of SE 8 , and then cooled to 30°C (cooling rate = 0.5°C min −1 ). A shear force (the range of shear distance = 0 to 5.0 mm) was applied to the film sample at 30°C (Fig. 6). The sample was exposed to an x-ray beam (λ = 1.0 Å) with an incident angle of 90°for through-view images (Fig. 6, A and C) or 1°for reflection images (Fig. 6, B and D). 2D XRD images were collected using an imaging-plate area detector.

GI-XRD measurements for film samples
2D XRD images of a film sample of SE 8 were measured using the BL-8A beamline at Photon Factory (Ibaraki, Japan). The film sample sandwiched between a sapphire substrate and a polyimide sheet with a 10-μm-thick spacer was heated once to the melting point of SE 8 on an Instec HTC-402 hot stage and subsequently cooled to −80°C. The polyimide sheet was peeled off at −80°C.
The obtained film was exposed to an incident x-ray beam (λ = 1.0 Å, incident angles = 0.1 to 0.4°) with an oscillation of 1.0°for each frame. The XRD images were collected using an imaging-plate area detector.

Computational details
AI-MD calculations for stacked dimer models of SE 1 and TE 1 were performed using the SIESTA program package (59). Initial geometries were used from each single-crystal structure. For the exchange correlation (XC) functional of density functional theory, van der Waals (vdW) correction functional, vdW-DF2 (60), and the single zeta plus polarization function-level basis set were used. To control temperature, Nose-Hoover thermostat was applied for MD. The validity of the adopted XC and basis set was confirmed by the fact that the calculation level successfully reproduced the lattice constants of the single crystal structure of SE 1 (experimental: a = b = 13.89 Å and c = 7.73 Å and calculation: a = b = 13.82 Å and c = 7.56 Å) and the distance between the stacked molecules (experimental: d = 3.87 Å and calculation: d = 3.88 Å). To accelerate MD, mass of hydrogen atom was replaced to that of tritium. The time step of MD was taken as 0.8 fs. Trajectories were calculated for about 10 ps, where those after 2.5 ps were used for sampling. To represent flexibility of deformation of the stacked structure, inclination angle was set as collective coordinate. PMF, i.e., free-energy profiles, were calculated as a function of θ.

Supplementary Materials
This PDF file includes: Figs. S1 to S17 Legends for movies S1 and S2 Other Supplementary Material for this manuscript includes the following: Movies S1 and S2